Ground-state clusters of two-, three-, and four-dimensional +/- J Ising spin glasses

A huge number of independent true ground-state configurations is calculated for two-, three- and four-dimensional +/-J spin-glass models. Using the genetic cluster-exact approximation method, system sizes up to N = 20(2),8(3),6(4) spins are treated. A ballistic-search algorithm is applied, which allows even for large system sizes to identify clusters of ground states that are connected by chains of zero-energy flips of spins. The number of clusters n(c) diverges with N going to infinity. For all dimensions considered here, an exponential increase of n(c) appears to be more likely than a growth with a power of N. The number of different ground states is found to grow clearly exponentially with N. A zero-temperature entropy per spin of s(o)=0.078(5)k(B) (2D), s(o) = 0.051(3)k(B) (3D), respectively, s(o) = 0.027(5)k(B) (4D) is obtained.